Question

stock prices are at their peak. here f is the stock price. then
○f(x)>0,f(x)>0
○f(x)=0,f(x)<0
○f(x)<0,f(x)=0
○f(x)=0,f(x)>0
○f(x)>0,f(x)=0
question help: video message instructor

Explanation:

Step1: Analyze the first - derivative condition

At a peak (local maximum) of a function \(y = f(x)\), the slope of the tangent line is zero. By the definition of the first - derivative (where \(f^{\prime}(x)\) represents the slope of the tangent line to the curve \(y = f(x)\) at the point \(x\)), we have \(f^{\prime}(x)=0\).

Step2: Analyze the second - derivative condition

The second - derivative \(f^{\prime\prime}(x)\) tells us about the concavity of the function. If \(f^{\prime\prime}(x)<0\), the function \(y = f(x)\) is concave down. At a local maximum, the function changes from increasing (concave up in some regions before the maximum in a general sense, but at the maximum point) to decreasing, and the concavity is such that the function is concave down. So \(f^{\prime\prime}(x)<0\) at a local maximum.

Answer:

\(f^{\prime}(x) = 0,f^{\prime\prime}(x)<0\)